How can I achieve a crystalline glaze material procedurally?
A favorite trick of mine is to mix a bit of noise into the coordinate vector.

You can use object coordinates here, it's not really important as long as you can make the masks you need.
What I ended up doing is generating several noise masks, some of them share the same nodes, I'm just using a Color Ramp to isolate different parts:




And used Math nodes to add and subtract them rather randomly:

And then I used a Math node set to Greater Than and played with the value until I found something I liked.

Using this as the factor input for a Mix Shader you can create the top and bottom materials to your liking.
My favorite detail of handmade objects like this is that they are rarely perfect.  We often model these objects to (float) precision, perfect all the way around.  So to add an almost imperceptible bit of realism I take a very lumpy Noise Texture and do just a tad of displacement.

Here is a render using these methods.  HDRI environment is Cayley Interior from HDRIHaven.  I'm using only Noise Textures for the base color layers.